Up and down cascades: three-dimensional magnetic field model

In our previous works we already have proposed a two-dimensional model of geodynamo. Now we use the same approach to build a three-dimensional self-excited geodynamo model that generates a large scale magnetic field from whatever small initial field, using the up and down cascade effects of a multiscale turbulent system of cyclones. The multiscale system of turbulent cyclones evolves in six domains of an equatorial cylindrical layer of the core. The appearance of new cyclones is realized by two cascades: a turbulent direct cascade and an inverse cascade of coupling of similar cyclones. The interaction between the different domains is effected through a direct cascade parameter which is essential for the statistics of the long-life symmetry breaking. Generation of the secondary magnetic field results from the interaction of the components of the primary magnetic field with the turbulent cyclones. The amplification of the magnetic field is due to the transfer of energy from the turbulent helical motion to the generated magnetic field. The model demonstrates a phase transition through the parameter characterizing this energy transfer. In the supercritical domain we obtain long-term intervals of constant polarity (chrons) and quick reversals; relevant time constants agree with paleomagnetic observations. Possible application of the model to the study of the geometrical structure of the geomagnetic field (and briefly other planetary fields) is discussed.